Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

There is a proof that I'm trying to understand, but the textbook I have isn't making any sense and my teachers explanations are not very clear to non-existent. I'm trying to understand why: $$x^4 - y^4 = z^2$$ has no solutions. I've found a proof of this theorem here, but there is little to no explanation as to why each step was taken. I was hoping someone out there who understands this proof well can explain it to me, or provide an alternative way to prove it.

share|cite|improve this question
up vote 2 down vote accepted

I usually first prove that if $x^2+y^2=z^2$ for some integers, then the right-angled triangle with sides $x,y,z$ cannot have square area. You can find a proof of that here: Pythagorean triples and perfect squares. Then if there is an integer solution to your equation, you can deduce a right-angled triangle with integer sides and square area.

You can also find a direct proof here: Solving $x^4-y^4=z^2$

share|cite|improve this answer
Alright thanks a lot! – Math_Illiterate Apr 19 '13 at 0:29

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.